This paper points out that the ARMA models followed by GARCH squares are volatile and gives explicit and general forms of their dependent and volatile innovations. The volatility function of the ARMA innovations is shown to be the square of the corresponding GARCH volatility function. The prediction of GARCH squares is facilitated by the ARMA structure and predictive intervals are considered. Further, the developments suggest families of volatile ARMA processes.
The paper presents local dynamic approach to integration of an ensemble of predictors. The classical fusing of many predictor results takes into account all units and takes the weighted average of the results of all units forming the ensemble. This paper proposes different approach. The prediction of time series for the next day is done here by only one member of an ensemble, which was the best in the learning stage for the input vector, closest to the input data actually applied. Thanks to such arrangement we avoid the situation in which the worst unit reduces the accuracy of the whole ensemble. This way we obtain an increased level of statistical forecasting accuracy, since each task is performed by the best suited predictor. Moreover, such arrangement of integration allows for using units of very different quality without decreasing the quality of final prediction. The numerical experiments performed for forecasting the next input, the average PM10 pollution and forecasting the 24-element vector of hourly load of the power system have confirmed the superiority of the presented approach. All quality measures of forecast have been significantly improved.